Chelsea maintained their unbeaten start to the season to move top of the Premier League as Leicester and Arsenal celebrated claiming maiden victories on Saturday.
First-half goals from Eden Hazard and Willian put the home side in charge against Burnley at Stamford Bridge before Victor Moses made absolutely certain of victory a minute from time.
That made it three wins out of three for Antonio Conte's side and took them clear at the top of the table with Manchester City not in action and Hull and Manchester United facing each other in the late kick-off.
Leicester secured the first win of their title defence with a 2-1 victory over Swansea, despite Riyad Mahrez missing a second-half penalty.
Jamie Vardy put Claudio Ranieri's side in front after 32 minutes.
Wes Morgan made it 2-0 early in the second half before Mahrez had the chance to seal the win from the spot.
However, Mahrez saw his effort saved by Swansea goalkeeper Lukasz Fabianski and Leroy Fer pulled a goal back 10 minutes from time to set up a nervous finish for the Foxes.
Arsenal eased the pressure on manager Arsene Wenger with a 3-1 win at Watford which was effectively sealed before the interval at Vicarage Road.
Santi Cazorla opened the scoring from the penalty spot after 10 minutes.
Alexis Sanchez doubled the lead five minutes before half-time.
Mesut Ozil then rubbed salt into Watford's wounds with a third in first-half stoppage time and although substitute Roberto Pereyra pulled one back after 57 minutes, Arsenal comfortably secured all three points.
David Moyes secured his first point as Sunderland manager with a 1-1 draw at Southampton, but will have been disappointed not to have claimed all three at St Mary's.
Jermain Defoe gave the visitors the lead from the penalty spot after 80 minutes.
But the Black Cats could not hold on to their advantage for long, with substitute Jay Rodriguez equalising five minutes later - his first Premier League goal in more than two years after serious injuries.
A penalty did prove decisive at Goodison Park as Everton moved second in the table thanks to a 1-0 victory over Stoke in fortunate circumstances.
After Ashley Williams had been brought down in the area by Phil Bardsley, Leighton Baines scuffed his 51st-minute penalty, but saw it come back off the post, hit goalkeeper Shay Given and cross the line.
Crystal Palace claimed their first point of the season with a last-minute equaliser against Bournemouth, who had taken the lead in the 11th minute through Joshua King.
Johan Cabaye saw his 16th-minute penalty saved by goalkeeper Artur Boruc and it looked as though the visitors would claim all three points until Scott Dann headed home in stoppage time.
In the day's early kick-off, Liverpool and Tottenham drew 1-1 at White Hart Lane after Danny Rose cancelled out James Milner's first-half penalty.